Ind. Eng. Chem. Fundam. 1986, 25, 211-216 Gutierrez, A.; Lynn, S. Ind. Eng. Chem. Process Des. D e v . 1868, 6, 486-49 1. Hooper, F. C.; Abdelmessih, A. H. I n “Proceedings of the 3rd Internatlomil Heat Transfer Conference, Chicago, 1966”; AIChE: New Ycfk, 1968: pp 44-50. Kitamura, Y.; Takahashi, T. I n “Proceedings of the 1st International Conference on Liquid Atomization and Spray Systems, Tokyo, 1978”; Fuel SocC ety of Japan: Tokyo, 1979; pp 1-7. Kosky, P. G. Chem. Eng. Sei. 1968, 23,695-706. Lackme, C. Int. J. Multiphase Flow 1879, 5, 131-141. Lienhard, J. H. Trans. ASME, Ser. D 1966, 88, 685-687. Lienhard, J. H.; Day, J. B. Trans. ASME, Ser. D 1970, 92, 515-522. Lienhard, J. H.; Stephenson, J. M. Trans. ASME, Ser. D 1968, 88, 525-532. Fujii, T.; Tanaka, T.; Nakaoka, T. Kagaku Kogaku Ronbunshu Miyatake, 0.; 1975, 1 , 393-398. Miyatake, 0.; Tomimura, S.; Ide, Y.; Fujii, T. Trans. SOC.Mech. Eng., Tokyo 1879, 45, 1863-1891. Plesset, M. S.; Zwick, S. A. J. Appl. Phys. 1954, 25, 493-500. Scriven, L. E. Chem. Eng. Sei. 1959, 10, 1-13.
21 1
fWr, E.; Elata, C. Id.Eng. Chem. Recess Des. Dev. 1877. 16, 237-242. Slmpson, S. G.; Lynn, S. AIChE J. 1877, 23. 888-679. S m , A. M.; Slelcher, C. A. J. FlUMh4ech. 1875, 68, 477-495. S u m , S.; Koizumi, M. Trans. SOC. Mech. Eng., Tokyo 1977, 43, 4608-4621. Suzuki, M.; Yamamoto, T. I n “Proceedings of the 1st International Confere n m on Liquid Atomization and Spray Systems, Tokyo, 1978”; Fuel Society of Japan: Tokyo, 1979; pp 37-43. Theofanous, T.; Biasi, L.; Isbin, H. S. Chem. Eng. Sei. 1969, 24,885-897. Tong, L. S. “Boiling Heat Transfer and Two-Phase Flow”; Wiley: New York, 1985; p 14. Weber, C. 2 . Angew. Math. Mech. 1931, 11, 136-154. Westwater, J. W. “Advances In Chemical Engineering”; Drew, T. B., Hoopes, J. W., Eds.; Academic Press: New York, 1956; p 2.
Received for review November 14, 1983 Revised manuscript received August 21, 1984 Accepted May 30, 1985
Equilibrium Disproportionation and Isomerization of Alkylbenzenes Robert A. Alberty Chemlshy Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
Equilibrium calculations on complex organic systems may be simplified by use of isomer groups, rather than individual species, and restricted Isomer groups may be used when the catalyst is selectlve. These methods are illustrated by calculations on the equilibrium disproportionation and isomerization of the alkylbenzenes at a series of H/C ratios. Comparison with data on the distribution of alkylbenzenes obtained in the conversion of methanol to gasoline using ZSM-5 illustrates the selectivity of the catalyst and the restricted equilibrium that does occur. The concept of isomer groups may be extended to whole homologous series by fixing the ethylene partial pressure. When this is done, the equilibrium distribution of isomer groups in a homologous series like the alkylbenzenes can be calculated with the same equation as used for the calculation of equilibrium mole fractions within an isomer group. The equilibrium partial pressure of ethylene is a function of the ratio of hydrogen to carbon for the homologous series. The use of this method, illustrated for the alkylbenzenes, has the additional advantage that it provides an indicator for the degree of alkylation of different homologous series in the same reaction system. Homologous series that are in equilibrium with the same partial pressure of ethylene are in equilibrium with each other.
Introduction In making equilibrium calculations on organic systems with many species, it is advantageous to use isomer group thermodynamic properties (Smith, 1959; Smith and Missen, 1982; Alberty, 1983a) because this reduces the number of “species” that have to be included in the calculation. In a second step the equilibrium mole fractions of individual species may be calculated if their Gibbs energies of formation are known. The use of isomer group thermodynamic properties has the additional advantage that thermodynamic properties of isomer groups with higher carbon numbers, where data on individual species are lacking, may be estimated by linear extrapolation (Alberty, 1983b; Alberty and Gehrig, 1984). If the catalyst is selective, the species that are not produced may be omitted from the calculation of isomer group properties. The concept of isomer groups may be extended to whole homologous series by incorporating the partial pressure of ethylene into the definition of the standard state for an isomer group in the homologous series (Alberty, 1985a). If the partial pressure of ethylene is fixed, the distribution of isomer groups within a homologous series becomes a function of temperature only; under these circumstances a homologous series behaves like an isomer group, and so we can call it a pseudoisomer group. This means that the same sort of equations which make it simple to calculate the distribution of species in an isomer group can be used 0 196-4313/86/1025-0211$0 1.50/0
to calculate the distribution of isomer groups in a homologous series group. Equilibria within a homologous series are independent of pressure because the various isomer groups can be equilibrated through disproportionation reactions; for example, for the alkylbenzenes 2CnHzn+ = Cn-lHzn-8 + Cn+lHZn-d
(1)
The equilibria within the alkene homologous series are an exception to this statement because of the volume change in the reaction (n/2)CzH4= C,Hzn at constant pressure. It is advantageous to calculate equilibrium compositions at fixed ethylene partial pressures because a general equilibrium computer program does not have to be used and because the partial pressure of ethylene provides a useful indicator of the extent of alkylation in the homologous series. In this paper these methods are used in calculating equilibrium distributions for the alkylbenzenes at various H/C ratios (or corresponding ethylene partial pressures). Equilibrium distributions of benzene and methylbenzenes have been calculated by Egan (1960) and by Hastings and Nicholson (1961), but in actual equilibria other alkylbenzenes are also present. Voltz and Wise (1976) have pointed out that the experimental distribution of some alkylbenzenes in the gasoline produced from methanol with zeolite ZSM-5 is in reasonable agreement with equilibrium calculated from disproportionation and isomerization. 0 1986 American Chemical Society
212
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
Table I. Standard Gibbs Energy of Formation for Alkylbenzene Isomer Groups (in kJ mol-') Calculated from Tables of Stull et al. increments Der carbon atom 298.15
300.00 400.00 500.00 600.00
700.00 800.00 900.00 1000.00
129.73 130.02 146.57 164.29 182.80 201.86 221.26 240.90 260.76
122.10 122.56 147.83 174.64 202.37 230.81 259.59 288.70 317.93
117.71 118.29 153.09 189.65 227.34 265.87 304.83 344.16 383.70
Two problems are encountered in calculating equilibrium distributions of alkylbenzenes in the ideal gas phase when species other than the methylbenzenes are included: (1)the number of isomers increases rapidly with the carbon number, and (2) literature data on individual alkylbenzene isomers up to 1000 K are complete only through C9Hl2 (Stull et al., 1969). The numbers of isomers, including stereoisomers, of the alkylbenzenes are as follows: C6H6, 1;C&, 1; C8H10,4; C9HI2,8; C10H14,23; CllH16, 46; and CI2Hl8,109. In the absence of literature data on all isomers above CgH12, the properties of isomers of C10H14 to ClzH18 have been calculated by using Benson group values (Alberty, 1985b). For still higher isomer groups thermodynamic properties can be estimated by linear extrapolation.
Theory When isomers are in equilibrium, the standard Gibbs is calculated energy of formation of an isomer group, from NI
AfCoI= -RT In [Cexp(-AfGo,/RT)]
(2)
1=1
where AGO, represents the standard Gibbs energies of formation of the NI isomers (including stereoisomers). The equilibrium mole fraction rt of isomer i within an isomer group is given by (3) rl = yl/yI = exp[(AfGoI- A&Oi)/RT] where y Lis the mole fraction of i and yI is the mole fraction of its isomer group. References to earlier uses of these equations are given by Smith and Missen (1982). In making equilibrium calculations, one may incorporate the partial pressure of ethylene into the definition of the standard state (Alberty, 1985a). To do this for the alkylbenzenes, the formation reaction is written
The Gibbs energy of formation for the isomer group CnHzf14for a standard state with a fixed value for the partial pressure of ethylene is given by AfG*I(CnH2nd = A&OI(CnHd ((n - 6 ) / 2 ) ( W 0 ( C ~ H 4+) RT In P(C2H4)) (5) At a fixed partial pressure of ethylene the successive isomer groups in the alkylbenzene homologous series are pseudoisomers because their distribution depends only on temperature. Therefore, we can calculate a Gibbs energy for the homologous series group (HSG) using the following analogue of eq 2. m
AfG*(HSG) = -RT In
C exp[-A&*I(CflHzn+)/RT] (6)
n=6
This quantity is of interest primarily because we can use it to calculate the equilibrium mole fraction for a particular
116.49 161.51 208.36 256.35 305.18 354.35 403.87 453.54
-7.46 1.26 10.35 19.56 28.95 38.33 47.80 57.18
-4.27 5.27 15.02 24.98 35.06 45.25 55.46 65.77
-1.81 8.42 18.71 29.01 39.31 49.51 59.71 69.84
isomer group within the alkylbenzene homologous series using r(CnHzn-s)= expl t AfG*(HSG) - W*1(CnH2n+)l/ R T ) (7) This method is more than a means for calculating equilibrium distributions in alkylation reactions because the equilibrium partial pressure can be used to relate the equilibria in different homologous series. Consider, for example, a system containing only alkanes and alkylbenzenes. If we want to calculate equilibrium compositions that correspond to different extents of alkylation, we can imagine adding ethylene to give the desired degree of alkylation. For purposes of the calculation the two homologous series can be considered separately in the first step. The degree of alkylation of the alkanes is a function of the partial pressure of ethylene, and the degree of alkylation of the alkylbenzenesis a different function of the partial pressure of ethylene. In order for a particular equilibrium composition of the alkanes to be in equilibrium with a particular equilibrium composition of the alkylbenzenes, they both have to have the same partial pressure of ethylene. We have here a kind of analogue to the zeroth law of thermodynamics. If homologous series A and B are in equilibrium with the same partial pressure of ethylene, then they are in equilibrium with each other.
Data for Equilibrium Calculations The standard Gibbs energies of formation of the alkylbenzene isomer groups CsHlo and CgH12in the ideal gas state, given in Table I in kJ mol-l for a standard-state pressure of 1bar, have been calculated from data in Stull et al. (1969). The values for the individual species basically come from tables of Rossini et al. (1953); the calculations were started by Pitzer and Scott (1943). Somayajulu (1983) has calculated Cpo, So,AfHo,and AfGo for the isomers of Cia14 at 298.15 K. His values for A&' average 3.6 kJ mol-l lower than those calculated by using the Benson method as described below. As shown in Table I the increments per carbon atom are still increasing with carbon number at C9H12,and this raises the question whether the dependence of A~GOIon carbon number is linear or quadratic. Therefore, the Benson (1976) method was used to estimate A&', for all the individual isomers of the alkylbenzenes up to CI2Hl8 in the ideal gas state using computer programs written in APL (Alberty, 1984). The numbers of the various Benson groups, total symmetry numbers, numbers of optical isomers, and numbers of ortho corrections were put in a matrix with a row for each structure. In view of uncertainties in some of the alkylbepene group values indicated by Benson, the gauche and 1,5-H repulsions, which affect only several of the most highly branched species, were omitted. The group assignments were checked by matrix multiplication to be sure they accounted for the correct
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986 213
Table 11. Standard Gibbs Energy of Formation for Alkylbenzene Isomer Groups (in kJ mol-') Calculated from Benson Group Values increments per carbon atom
clz-cll 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
130.11 146.69 164.46 183.09 202.27 221.86 241.64 261.57
121.83 147.02 173.72 201.53 230.06 259.11 288.42 317.92
116.73 151.46 187.94 225.70 264.26 303.40 342.79 382.38
115.01 159.91 206.62 254.59 303.35 352.66 402.19 451.88
117.31 172.20 228.78 286.64 345.32 404.59 464.08 523.74
122.18 187.00 253.53 321.45 390.28 459.78 529.55 599.50
125.72 199.57 275.76 353.72 432.77 512.60 592.74 673.09
-8.28 0.33 9.27 18.45 27.79 37.25 46.77 56.35
-5.10 4.43 14.22 24.17 34.20 44.29 54.38 64.46
-1.72 8.45 18.67 28.89 39.09 49.26 59.40 69.50
2.30 12.29 22.16 32.05 41.97 51.93 61.89 71.86
3.39 3.55 12.57 22.24 32.27 42.49 52.82 63.19 73.59
4.86 14.81 24.75 34.80 44.96 55.19 65.47 75.76
Table 111. Parameters for Calculating the Standard Gibbs Energy of Formation at N > 12
T/K A/kJ mol-' B/kJ mol-'
298.15 76.202 4.034
300 75.481 4.205
400 35.697 13.687
500 -5.732 23.493
600 -48.292 33.536
700 -91.502 43.724
800 -135.078 54.006
900 -178.835 64.329
1000 -222.677 74.678
Table IV. Equilibrium Mole Fractions of Alkylbenzene Isomer Groups for Six H/C Ratios at 700 K H/C 1.143 0.319 0.427 0.199 0.045 0.009 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.250 0.086 0.284 0.330 0.184 0.089 0.019 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.333 0.024 0.133 0.260 0.245 0.200 0.071 0.039 0.016 0.007 0.003 0.001 0.001 0.000 0.000 0.000
numbers of carbon and hydrogen atoms. The matrix of numbers of contributions was then matrix-multiplied by the matrix of Benson group values to obtain for each isomer the s u m of the contributions to 4Hom,Sintom, CPom, CPom, Cpo500,CPorn, C p o ~ o opol^, , and C p o l ~These values, the total symmetry numbers, and the numbers of optical isomers were then used to calculate the standard Gibbs energy of formation of each species (or racemate of chiral isomers) at 298.15, 300,400,500,600,700,800,900, and 1000 K. The standard Gibbs energies of formation of benzene, toluene, and the alkylbenzene isomer groups calculated by using the Benson method are given in Table 11. These values for C6H6to C9H12pre in very good agreement with the values calculated from Stull et al. (1969) given in Table I. The increments in A @ O 1 per carbon atom continue to increase to CllH16, but the increments Cl1-Cl0and C12-C11 are nearly enough the same that values for C10H14, CllH16, and C12Hls were least-squared to determine A and B in AfGOI = A + Bn, where n is the number of carbon atoms. The values of A and B given in Table I11 were then used to estimate A @ O I for isomer groups C13H20to CmHw The standard Gibbs energies of formation used in calculations of disproportionation equilibria in this paper came from the following sources: C6H6to C9H12, Stull et al. (1969); C10H14 to C12H18, the Benson (1976) method; C12Hzoto CtoH,, linear extrapolation of values calculated by using the Benson method. Calculation of Equilibrium Compositions In order to calculate the equilibrium mole fractions of alkylbenzene isomer groups up to C20H34 at a particular
1.400 0.008 0.064 0.168 0.214 0.236 0.114 0.084 0.047 0.028 0.017 0.010 0.006 0.004 0.002 0.001
1.455 0.004 0.034 0.109 0.165 0.217 0.125 0.110 0.073 0.052 0.037 0.026 0.019 0.013 0.009 0.007
1.500 0.002 0.020 0.071 0.123 0.182 0.118 0.117 0.088 0.070 0.056 0.045 0.036 0.029 0.023 0.019
temperature and H/C ratio, a general equilibrium computer program can be used. These calculations were made using EQUCALC, an APL function written by Fred Krambeck (1978) in which the system of nonlinear algebraic equations is solved using the Newton-Raphson procedure. Calculations have been made for H/C = 1.142, 1.25, 1.333, 1.4, 1.455, and 1.5 (corresponding with starting material of C ~ H BGHio, , CgHi2, CioHi4, CiiHi6, and Ci2Hi8), but calculations can be made for any H/C ratio in the range 1< H/C < 2. However, as H/C is increased above about 1.5, isomer groups above C20H3,have to be included in the calculation at 700 K. Table IV gives the calculated distribution in the ideal gas phase at 700 K for the six H/C ratios. This table shows why it is necessary to include higher isomer groups in calculations at H/C ratios above about 1.5. The calculated values can represent real systems only if the mole fractions of higher isomer groups decrease asymptotically to negligible values at the highest carbon number included in the calculation. Since possible errors in the extrapolation from C10H14, CllH16, and Cl2Hl8 are already significant at C20H34, these calculations have not been extended beyond about H/C = 1.5. Table IV has been expanded to Table V to show the calculated equilibrium mole fractions of individual species. This has been done by multiplying the equilibrium mole fractions of the various isomer groups by the equilibrium mole fractions ri of the individual species with the isomer groups, given by eq 3. However, since the expanded table has 200 lines, it has been shortened by omitting the species with the smallest mole fractions. The sums of the mole fractions of the species shown in Table V are given in the last line. This table is of interest because it shows the
214
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
Table V. Equilibrium Mole Fractions of Alkylbenzenes for Six H/C Ratios at 700 K
H/C C6H6
C7H8
C8HlO
ethylbenzene 1,3-dimethylbenzene 1,2-dimethylbenzene 1,4-dimethylbenzene C9Hn propylbenzene isopropylbenzene 1-ethyl-3-methylbenzene 1-ethyl-2-methylbenzene 1-ethyl-4-methylbenzene 1,2,3-trimethylbenzene 1,2,4-trimethylbenzene 1,3,5-trimethylbenzene
1.143 0.319 0.427
1.250 0.086 0.284
1.333 0.024 0.133
1.400 0.008 0.064
1.455 0.004 0.034
1.500 0.002 0.020
0.017 0.095 0.044 0.043
0.028 0.157 0.073 0.071
0.022 0.124 0.058 0.056
0.014 0.080 0.037 0.036
0.009 0.052 0.024 0.023
0.006 0.034 0.016 0.015
0.001 0.000 0.007 0.003 0.005 0.002 0.019 0.007
0.004 0.002 0.011 0.019 0.010 0.079 0.030
0.005 0.002 0.039 0.014 0.025 0.013 0.105 0.040
0.004 0.002 0.034 0.013 0.022 0.012 0.092 0.035
0.003 0.002 0.026 0.010 0.017 0.009 0.071 0.027
0.003 0.001 0.020 0.007 0.013 0.007 0.053 0.020
0.002 0.001 0.001 0.006 0.016 0.010 0.003 0.008 0.008 0.002 0.008 0.013 0.001 0.003 0.002 0.001 0.003 0.002 0.001 0.001
0.003 0.001 0.002 0.014 0.035 0.022 0.007 0.018 0.018 0.004 0.018 0.028 0.002 0.006 0.004 0.002 0.006 0.004 0.001 0.001
0.004
0.004 0.001 0.002 0.015 0.038 0.023 0.008 0.020 0.020 0.005 0.020 0.031 0.003 0.007 0.004 0.003 0.007 0.004 0.002 0.001
0.003 0.001 0.002 0.013 0.032 0.020 0.006 0.017 0.017 0.004 0.017 0.026 0.002 0.005 0.003 0.002 0.006 0.003 0.001 0.001
0.002 0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.001
0.007 0.003 0.009 0.003 0.005 0.005 0.003 0.003 0.004 0.003 0.003 0.003 0.003 0.003 0.002 0.001 0.001 0.001 0.003 0.001 0.001 0.001 0.001 0.001 0.001 0,001 0.001 0.001 0.001 0.016 0.007 0.003 0.001 0.001 0.000 0.000 0.000 0.960
0.010 0.005 0.014 0.005 0.008 0.008 0.004 0.004 0.007 0.004 0.005 0.005 0.005 0.005 0.003
0.011 0.006 0.015 0.006 0.009 0.009 0.005 0.005 0.007 0.005 0.005 0.005 0.005 0.005 0.003 0.003 0.004 0.004 0.003 0.009 0.003 0.003
0.011 0.006 0.014 0.006 0.009 0.009 0.004 0.004 0.007 0.004 0.005 0.005 0.005 0.005 0.003 0.003 0.004 0.004 0.003 0.009 0.004 0.004
0.003
0.004
0.003 0.004 0.004 0.004 0.003 0.003 0.073 0.052 0.037 0.026 0.019 0.013
0.004 0.004 0.004 0.004 0.003 0.004 0.088
0.029
C10H14
1,3-diethylbenzene 1,2-diethylbenzene l,4-diethylbenzene 1,2,3,4-tetramethylbenzene 1,2,3,5-tetramethyibenzene 1,2,4,5-tetramethylbenzene l-ethyl-2,3-dimethylbenzene l-ethyl-2,4-dimethylbenzene l-ethyl-2,5-dimethylbenzene l-ethyl-2,6-dimethylbenzene l-ethyl-3,4-dimethylbenzene l-ethyl-3,5-dimethylbenzene 1-propyl-2-methylbenzene 1-propyl-3-methylbenzene 1-propyl-4-methylbenzene 1-isopropyl-2-methylbenzene 1-isopropyl-3-methylbenzene 1-isopropyl-4-methylbenzene 2-methylpropylbenzene l(RS)-methylpropylbenzene
0.000 0.000 0.000 0.001 0.002 0.001 0.000 0.001 0.001 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
C11H16
pentamethylbenzene l-ethyl-2,3,4-trimethylbenzene l-ethyl-2,3,5-trimethylbenzene l-ethyl-2,3,6-trimethylbenzene l-ethyl-2,4,6-trimethylbenzene l-ethyl-3,4,5-trimethylbenzene 1,2-diethyl-4-methylbenzene 1,3-diethyl-4-methylbenzene 1,3-diethyl-5-methylbenzene 1,4-diethyl-P-methylbenzene l-propyl-2,4-dimethylbenzene l-propyl-2,5-dimethylbenzene l-isopropyl-2,4-dimethylbenzene l-isopropyl-2,5-dimethylbenzene 1-(l(RS)-methylpropy1)-3-methylbenzene 1-isobutyl-3-methylbenzene l-ethy1-2,3,4,5-tetramethylbenzene l-ethy1-2,3,4,6-tetramethylbenzene l-ethy1-2,3,5,6-tetramethylbenzene 1,2-diethyl-3,5-dimethylbenzene 1,3-diethyl-2,5-dimethylbenzene 1,3-diethyl-4,5-dimethylbenzene 1,4-diethyl-2,5-dimethylbenzene 1,4-diethyl-2,5-dimethylbenzene l-propyl-2,4,5-trimethylbenzene l-isopropyl-2,3,5-trimethylbenzene l-isopropyl-2,4,5-trimethylbenzene 1-(1(RS)-methylpropyl)-3,5-dimethylbenzene 1-isobutyl-3,5-dimethylbenzene C13H20 C14H22 C15H24
C16H26
C,,H,, C18H30 Cl9H3,
GoH,, total
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 000 I
0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.997
0.001
0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.992
0.002
0.002 0.016 0.042 0.025 0.008 0.021 0.021 0.005 0.021 0.033 0.003 0.007 0.004 0.003 0.007 0.004 0.002 0.002
0.003
0.003 0.003 0.002 0.006 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.003 0.047 0.028 0.017 0.010 0.006 0.004 0.002
0.009
0.001 0.935
0.007 0.919
0.070
0.056 0.045 0.036 0.029 0.023 0.019 0.916
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
215
Table VI. Equilibrium Mole Fractions of a Restricted Set of Alkylbenzenes at 700 K Compared with Experimental Data on the Conversion of Methanol to Gasoline Using ZSM-5 at 679 K
benzene toluene ethylbenzene 1,3-dimethylbenzene 1,2-dimethylbenzene 1,4-dimethylbenzene 1-ethyl-4-methylbenzene 1,2,4-trimethylbenzene 1,4-diethylbenzene 1,2,4,5-tetramethylbenzene pentamethylbenzene
1.143 0.296 0.442 0.019 0.110 0.051 0.050 0.006 0.025 0.000 0.001 0.000
1.250 0.042 0.233 0.038 0.217 0.101 0.098 0.044 0.185 0.003 0.032 0.006
equilibrium distributions expected for a nonselective catalyst. Table V may be used to assess the extent to which the alkylbenzenes produced in the conversion of methanol to gasoline using zeolite ZSM-5 are in equilibrium with each other at the time the product is removed. In the Mobil base case at 679 K (Kam and Lee, 1978) the mole fractions within the alkylbenzenes were as follows: benzene, 0.010; toluene, 0.033; ethylbenzene, 0.017; 1,3- plus 1,4-dimethylbenzenes, 0.295; 1,2-dimethylbenzene,0.086; 1,2,4trimethylbenzene, 0.295; 1,3,5-trimethylbenzene, 0.019; l-ethyl-4-methylbenzene, 0.053; propylbenzene, 0.002; 1,2,4,5-tetramethylbenzene(durene), 0.105; 1,2,3,5-tetramethylbenzene, 0.031; 1,2,3,4-tetramethylbenzene, 0.012; l,Cdiethylbenzene, 0.028; pentamethylbenzene, 0.015. These values may be compared with the values in Table V, even though there is a 21 K difference in temperature, since the calculated equilibrium distribution does not change very rapidly with the temperature. The H/C ratio for this mixture of alkylbenzenes is 1.306. The ZSM-5 catalyst produces significantly more 1,2,4-trimethylbenzene, 1,4-diethylbenzene, and 1,2,4,5-tetramethylbenzene than would be expected from Table V and considerably less of other CloH,, and higher alkylbenzenes. This is a clear example of the shape selectivity of the zeolite catalyst. The concept of isomer groups may be used in equilibrium calculations with shape-selective catalysts in the following way: if the catalyst does not provide kinetic pathways to certain isomers in a group, these isomers are omitted in the calculation of the isomer group thermodynamic properties. Similarly, in calculating the equilibrium distribution between isomer groups of various carbon number, one may omit higher isomer groups if the catalyst does not provide kinetic pathways to those higher isomer groups. A restricted equilibrium calculation at 700 K for comparison with the methanol-to-gasoline conversion on ZSM-5 is shown in Table VI for five H/C ratios. Species which were not detected analytically were omitted from the calculation because it is assumed that the catalyst does not open up catalytic pathways to them. In addition, three species were omitted even though they were detected in the 0.01-0.03 mole fraction range within the alkylbenzenes. The reasons are as follows: 1,3,5-trimethylbenzene was omitted because at equilibrium it would be expected to have a mole fraction of about one-third that of 1,2,4-trimethylbenzene. Since the mole fraction in the Mobil base case is 5 times smaller than expected, the presumption is that 1,3,5-trimethylbenzene is formed by pathways with relatively low rate constants. Similarly, the experimental mole fractions of 1,2,3,4-tetramethylbenzeneand 1,2,3,5tetramethylbenzene are 5 times lower than expected from the experimental mole fraction of 1,2,4,5-tetramethyl-
1.292 0.011 0.113 0.033 0.189 0.088 0.085 0.068 0.286 0.010 0.088 0.029
1.333 0.003 0.046 0.023 0.128 0.060 0.058 0.078 0.327 0.018 0.168 0.091
1.400 0.000 0.004 0.005 0.030 0.014 0.013 0.048 0.200 0.029 0.271 0.386
exptl 0.011 0.035 0.018 0.218 0.092 0.097 0.057 0.316 0.029 0.111 0.016
Table VII. Partial Pressures (in bar) of Ethylene Equilibrium with Alkylbenzenes H/C T/K 1.143 1.250 1.333 1.400 1.455 Complete Isomer Groups 600 0.0001 0.0008 0.0027 0.0540 0.0080 700 0.0031 0.0190 0.0542 0.0989 0.1410 800 0.0345 0.1890 0.4910 0.8720 1.2600 600 700 800
0.0001 0.0038 0.0446
in
1.500 0.0104 0.1790 1.6400
Restricted Isomer Groups 0.0016 0.0162 0.0534 0.4780 0.6000 5.0100
benzene (durene), and so they were omitted on the basis that they are produced so slowly that they are not equilibrated with other species included in the calculation. Table VI shows that this restricted equilibrium calculation yields very nearly the experimental mole fractions at H/C = 1.306. The species included in the calculation account for 93.7% of the moles of alkylbenzenes in the base case. The calculation indicates there should be more toluene at equilibrium, but actually most conversion experiments show a lot more toluene than the base case.
Ethylene as an Indicator of the H/C Ratio The results given in Tables IV-VI can be obtained by fixing the partial pressure of ethylene and using eq 7, but an iteration is required to obtain a particular H/C ratio. However, if the objective is to determine whether an observed distribution is in agreement with thermodynamic equilibrium for all the members of an homologous series, or a particular subset, the ethylene partial pressure is a useful independent variable, and a general equilibrium program is not required. The equilibrium partial pressures of ethylene that correspond with the H/C ratios of previous tables were calculated at 600,700, and 800 K and are given in Table VII. Values are given for both complete isomer groups and for the restricted isomer groups of Table VI. These calculations were made with EQuCALC for systems that initially contained a mole of benzene and various amounts of ethylene, with only alkylbenzenes and ethylene as possible products. Since the alkylbenzene disproportionation equilibria are independent of pressure, the calculations were made at a sufficiently high pressure to cause almost all of the ethylene to react with the benzene to form alkylbenzenes. As the total pressure is increased, the partial pressure of ethylene approaches a value which is characteristic of the distribution of the alkylbenzenes at that temperature and H/C ratio. The experimentally determined partial pressure of ethylene in the methanol-togasoline conversion at 679 K is 0.044bar (Kam and Lee, 1978). The calculations with complete isomer groups summarized in Table VII yield very nearly this value. The
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Chern. Fundarn., Vol. 25, No. 2, 1986
calculations with the restricted isomer group yield higher values apparently because of the omission of species with higher carbon numbers. Calculations were not made at H/C = 1.454 because a t this ratio CllH16 would have a mole fraction of unity and the concept of an equilibrium partial pressure of ethylene becomes meaningless. As described in the Theory section, the partial pressure of ethylene is a useful handle in connecting the alkylation equilibria of different homologous series with each other. If several homologous series are in equilibrium with each other, they must have the same equilibrium partial pressure of ethylene. Conclusions The Benson method, which gives excellent agreement with the literature values for AfGoi for the alkylbenzenes C6&, C7H8,C8Hlo,and C9H12,indicates that the increment per carbon in AfGoI is essentially constant for C10H14, CllH16, and C12H18so that properties for higher isomer groups can be estimated by linear extrapolation. The distributions of alkylbenzenes expected at equilibrium with a nonselective catalyst have been calculated at 700 K in terms of individual species from C6H6through Cl2HI8and isomer groups from Cl3Hz0to C20H34.Experimental data on the conversion of methanol to gasoline using ZSM-5 catalysts indicate the shape selectivity of the catalyst for the alkylbenzenes. Some of the alkylbenzenes produced in the methanol conversion are in equilibrium with each other. Equilibria achieved with nonselective catalysts would yield different mole fractions of certain C9H12and C10H14alkylbenzenes and more of higher alkylbenzenes at the H/C ratios of the methanol conversion. The equilibrium partial pressure of ethylene is an indicator of the H/C ratio for an equilibrium mixture of alkylbenzenes and may also be used as an indicator for the H/C ratios of equilibrium mixtures of alkanes and alkylnaphthalenes and for the degree of polymerization of alkenes, cyclopentanes, and cyclohexanes. Thus, complete or restricted equilibrium calculations on these separate homologous series may be tied together through the ethylene partial pressure. Equilibrium calculations can be used to predict the effect of temperature, pressure, and composition on the mole fractions of species in rapid equilibrium, but rate constants have to be brought in to account for the mole fractions of certain species. Acknowledgment This research was supported by a grant from the Office of Basic Energy Sciences of the Department of Energy. The calculations have been made on the IBM 370/168 computer at the MIT Computing Center using programs written in APL. I am indebted to Catherine Gehrig for checking the Benson groups assignments. Nomenclature A , B = empirical parameters, kJ mol-’ AfGoi = standard Gibbs energy of formation of isomer i, kJ mol-’ A&O, = standard Gibbs energy of formation of isomer group I, kJ mol-’ n = number of carbon atoms in a molecule
NI = number of isomers in an isomer group rr = equilibrium mole fraction of i within its isomer group y i = equilibrium mole fraction of isomer i yI = equilibrium mole fraction of isomer group I Registry No. Ethylbenzene, 100-41-4;1,3-dimethylbenzene, 108-38-3; 1,2-dimethylbenzene, 95-47-6; 1,4-dimethylbenzene, 106-42-3;propylbenzene, 103-65-1;isopropylbenzene, 98-82-8; l-ethyl-3-methylbenzene,620-14-4; l-ethyl-2-methylbenzene, 611-14-3; l-ethyl-4-methylbenzene,622-96-8; 1,2,3-trimethylbenzene, 626-73-8; 1,2,4-trimethylbenzene,95-63-6; 1,3,5-trimethylbenzene, 108-67-8;1,3-diethylbenzene, 141-93-5;1,2-diethylbenzene, 135-01-3; 1,4-diethylbenzene,105-05-5; 1,2,3,4tetramethylbenzene, 488-23-3;1,2,3,5-tetramethylbenzene,52753-7; 1,2,4,5-tetramethylbenzene,95-93-2;l-ethyl-2,3-dimethylbenzene, 933-98-2; l-ethyl-2,4-dimethylbenzene, 874-41-9; 1ethyl-2,5-dimethylbenzene,1758-88-9; l-ethyl-2,6-dimethylbenzene, 2870-04-4; l-ethyl-3,4-dimethylbenzene, 934-80-5; 1ethyl-3,5-dimethylbenzene, 934-74-7;l-propyl-2-methylbenzene, 1074-17-5; l-propyl-3-methylbenzene,1074-43-7; l-propyl-4methylbenzene, 1074-55-1;l-isopropyl-2-methylbenzene, 527-84-4; l-isopropyl-3-methylbenzene,535-77-3; 1-isopropyl-4-methylbenzene, 99-87-6; (2-methylpropyl)benzene, 538-93-2; (&)-(lmethylpropyl)benzene,36383-15-0;pentamethylbenzene,700-12-9; l-ethyl-2,3,4-trimethylbenzene,61827-86-9; l-ethyl-2,3,5-trimethylbenzene, 18262-85-6; l-ethyl-2,3,6-trimethylbenzene, 61827-87-0; l-ethyl-2,4,6-trimethylbenzene, 3982-67-0; l-ethyl3,4,5-trimethylbenzene,31366-00-4;1,2-diethyl-4-methylbenzene, 13732-80-4; 1,3-diethyl-4-methylbenzene,1758-85-6; 1,3-diethyl&methylbenzene, 2050-24-0;1,4-diethyl-2-methylbenzene, 13632-94-5;2,4-dimethyl-l-propylbenzene,61827-85-8; 2,5-dimethyl-1-propylbenzene, 3042-50-0; l-isopropyl-2,4-dimethylbenzene, 4706-89-2;l-isopropyl-2,5-dimethylbenzene,4132-72-3; (i)-l-(l-methylpropyl)-3-methylbenzene, 100571-16-2; l-isobutyl-3-methylbenzene, 5160-99-6; l-ethy1-2,3,4,5-tetramethylbenzene, 31365-99-8; l-ethyl-2,3,4,6-tetraethylbenzene,4121674-4; l-ethy1-2,3,4,6-tetramethylbenzene, 31365-98-7; 1,2-diethyl-3,5-dimethylbenzene,96857-29-3; 1,3-diethyl-2,5-dimethylbenzene, 71766-58-0; 1,3-diethyl-4,5-dimethylbenzene, 94991-44-3;1,4-diethyl-2,5-dimethylbenzene, 39144-22-4; l-isobutyl-3,5-dimethylbenzene,98857-19-1; l-propyl-2,4,5-trimethylbenzene, 91647-78-8;l-isopropyl-2,3,5-trimethylbenzene, 41314-13-0; l-isopropyl-2,4,5-trimethylbenzene,10222-95-4; (i)-l-(l-methylpropyl)-3,5-dimethylbenzene, 100571-17-3. Literature Cited Alberty, R. A. Ind. Eng. Chem. Fundam. 1983a, 22, 318. Alberty, R. A. J . Phys. Chem. 1983b, 87, 4999. Alberty, R. A. J . Phys. Chem. 19858, 8 9 , 880. Aiberty, R. A. J . Phys. Chem. Ref. Data 1985b, 74. Aiberty, R. A.; Gehrig, C. J . Phys. Chem. Ref. Data 1984, 13, 1173. Benson, S. W. “Thermochemical Kinetics”; Wiiey: New York, 1976. Egan, C. J. J . Chem. Eng. Data 1960, 5, 298. Hastings, S. H.; Nicholson, D. E. J . Chem. Eng. Data 1961, 6 , 1. Kam, A. Y.; Lee, W. Report FE-2490-15, Department of Energy, 1978. Krambeck, F. J., paper presented at the 71st Annual Meeting of the American Instiiute of Chemical Engineers, Miami Beach, FL, Nov 16, 1978. Pitzer, K. S.; Scott, D. W. J . Am. Chem. SOC.1943, 65, 803. Rossini, F. D.; Pitzer, D. S.; Arnett, R. L.; Braun, R. M.; Pimentel, G. G. “Selected Values of Physical and Thermodynamic Properties of Hydrccarbons and Related Compounds”; Carnegie Press: Pittsburgh, 1953. Smith, B. D. AIChE J . 1959, 5 , 26. Smith, W. R.; Missen, R. W. “Chemical Reaction Equilibrium Analysis: Theory and Algorithms”; Wiley-Interscience: New York, 1982. SomayaJulu. G. R . Thermodynamics Research Center Hydrocarbon Project, Texas A&M University, College Station, TX, 1983. Stull, D. I?.;Westrum, E. F.; Sinke, G. C. “The Chemical Thermodynamics of Organic Compounds“; Wiley: New York, 1969. Voltz, S. E.; Wise, J. J. Report FE-1773-25, Energy Research and Development Administration, 1976.
Received for review January 16, 1984 Revised manuscript received April 15, 1985 Accepted June 25, 1985
